×
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.4 - Problem 17e
Get Full Access to Statistics For Engineers And Scientists - 4 Edition - Chapter 4.4 - Problem 17e

×

# Let X ~ Geom(p), let n be a non-negative integer, and let

ISBN: 9780073401331 38

## Solution for problem 17E Chapter 4.4

Statistics for Engineers and Scientists | 4th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Statistics for Engineers and Scientists | 4th Edition

4 5 1 308 Reviews
14
5
Problem 17E

Let $$X$$ ∼ Geom(p), let $$n$$ be a non-negative integer, and let $$Y$$ ∼ Bin(n, p). Show that P(X = n) = (1/n)P(Y = 1).

Equation Transcription:

Text Transcription:

X

n

Y

Step-by-Step Solution:

Solution :

Step 1 of 1:

Given and

Where mean  and variance .

Here non-negative integer is n.

Our goal is :

We need to prove that P(X=n)=.

Now we have to prove that P(X=n)=.

P(X=n)=

The formula of the geometric distribution is

P(X=n)=

Where q = (1-p)

So P(X=n)=

Then,

P(X=n)=

The formula of the binomial distribution is

Here the probability of X is n and the probability of Y is 1.

P(X=n)=

Here and = p.

P(X=n)=

Therefore P(X=n)=.

Step 2 of 1

## Discover and learn what students are asking

Calculus: Early Transcendental Functions : Inverse Trigonometric Functions: Integration
?In Exercises 1-20, find the indefinite integral. $$\int \frac{t}{\sqrt{1-t^{4}}} d t$$

Calculus: Early Transcendental Functions : Second-Order Homogeneous Linear Equations
?Finding a General Solution In Exercises 5-30,find the general solution of the linear differential equation. y’’ + 2y' = 0

Statistics: Informed Decisions Using Data : The Five-Number Summary and Boxplots
?What does the five-number summary consist of?

Statistics: Informed Decisions Using Data : Inference about the Difference between Two Medians: Dependent Samples
?In Problems 3–10, use the Wilcoxon matched-pairs signedranks test to test the given hypotheses at the a = 0.05 level of significance. The dependent sa

#### Related chapters

Unlock Textbook Solution